List questions from eigenvalues-eigenvectors

Published on 26 May 2018 - 11:23

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Eigenvectors of eigenvectors of eigenvectors of...

Published on 26 May 2018 - 15:29

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Prove that every square matrix $A^2 = I$ has at least one of the eigenvalues $\pm 1$ and no other eigen values

Published on 28 Mar 2026 - 17:40

381

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For a matrix, how to prove its max eigenvalue max inner product with any matrix which is semidefinite and has a trace less than 1?

Published on 24 Mar 2026 - 23:45

2.6k

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Orthogonality of eigenvectors of a Hermitian matrix

Published on 27 May 2018 - 5:34

187

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Prove that $HAH^{-1} = \left( \begin{smallmatrix} \lambda_{1} & b^{t} \\ 0 & B \\ \end{smallmatrix} \right) $

Published on 25 Mar 2026 - 6:27

125

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Calculating eigenvectors when eigenvalues is know

Published on 27 May 2018 - 14:50

1k

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Operator norm of a self adjoint operator.

Published on 25 Mar 2026 - 17:38

937

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Show that arbitrary $A$ and $A^T$ have same eigenvalue, algebraic and geometric multiplicity

Published on 25 Mar 2026 - 7:42

71

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Eigenvalue problem

Published on 25 Mar 2026 - 9:44

44

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Orthogonal bases for the eigenspaces.

Published on 27 Mar 2026 - 6:05

159

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How to prove that if $AB = A + B$ then $\frac{\lambda}{\lambda - 1}$ is an eigenvalue for $A$?

Published on 28 May 2018 - 17:36

221

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On vectors shifted by $1$?

Published on 28 Mar 2026 - 4:10

367

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Jordan Normal Form of $T:V\rightarrow V$ if $T^2$ is self adjoint

Published on 25 Mar 2026 - 12:27

34

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Be $n \in \mathbb N$ and $A \in Mat(n \times n, \mathbb C)$ with real entries and be $A^t = A$.

Published on 29 May 2018 - 14:14

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Does this matrix have one eigenvalue or two?

Eigenvectors of eigenvectors of eigenvectors of...

Prove that every square matrix $A^2 = I$ has at least one of the eigenvalues $\pm 1$ and no other eigen values

For a matrix, how to prove its max eigenvalue max inner product with any matrix which is semidefinite and has a trace less than 1?

Orthogonality of eigenvectors of a Hermitian matrix

Prove that $HAH^{-1} = \left( \begin{smallmatrix} \lambda_{1} & b^{t} \\ 0 & B \\ \end{smallmatrix} \right) $

Calculating eigenvectors when eigenvalues is know

Operator norm of a self adjoint operator.

Show that arbitrary $A$ and $A^T$ have same eigenvalue, algebraic and geometric multiplicity

Eigenvalue problem

Orthogonal bases for the eigenspaces.

How to prove that if $AB = A + B$ then $\frac{\lambda}{\lambda - 1}$ is an eigenvalue for $A$?

On vectors shifted by $1$?

Jordan Normal Form of $T:V\rightarrow V$ if $T^2$ is self adjoint

Be $n \in \mathbb N$ and $A \in Mat(n \times n, \mathbb C)$ with real entries and be $A^t = A$.

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